Chirality is a fascinating phenomenon that can manifest itself in subtle ways, for example in biochemistry (in the observed single-handedness of biomolecules) and in particle physics (in the charge-parity violation of electroweak interactions). In condensed matter, magnetic materials can also display single-handed, or homochiral, spin structures. This may be caused by the Dzyaloshinskii-Moriya interaction, which arises from spin-orbit scattering of electrons in an inversion-asymmetric crystal field. This effect is typically irrelevant in bulk metals as their crystals are inversion symmetric. However, low-dimensional systems lack structural inversion symmetry, so that homochiral spin structures may occur. Here we report the observation of magnetic order of a specific chirality in a single atomic layer of manganese on a tungsten (110) substrate. Spin-polarized scanning tunnelling microscopy reveals that adjacent spins are not perfectly antiferromagnetic but slightly canted, resulting in a spin spiral structure with a period of about 12 nm. We show by quantitative theory that this chiral order is caused by the Dzyaloshinskii-Moriya interaction and leads to a left-rotating spin cycloid. Our findings confirm the significance of this interaction for magnets in reduced dimensions. Chirality in nanoscale magnets may play a crucial role in spintronic devices, where the spin rather than the charge of an electron is used for data transmission and manipulation. For instance, a spin-polarized current flowing through chiral magnetic structures will exert a spin-torque on the magnetic structure, causing a variety of excitations or manipulations of the magnetization and giving rise to microwave emission, magnetization switching, or magnetic motors.

Combining relativistic first-principles calculations with a micromagnetic model, we establish the Dzyaloshinskii-Moriya interaction as an important mechanism in thin-film magnetism, determining the orientation of magnetic domains relative to the lattice, the type of domain wall, and the rotational direction of the magnetization in the wall. Applying the analysis to two monolayers Fe on W͑110͒, we provide an explanation for puzzling experimental data obtained by spin-polarized scanning tunneling microscopy. DOI: 10.1103/PhysRevB.78.140403 PACS number͑s͒: 75.70.Ak, 71.15.Mb, 75.60.Ch Understanding the nature of domains and domain walls in magnetic nanostructures has become an important issue in the field of spintronics as the controlled motion of domain walls opens up vistas for new types of memory and logic devices ͑e.g., Refs. 1 and 2͒. Domain walls in nanostructures and thin films are known to originate from the interplay of the quantum-mechanical exchange interaction ͑also expressed as spin stiffness͒, the magnetocrystalline anisotropy caused by the relativistic spin-orbit coupling ͑SOC͒, and the classical long-ranged magnetostatic contribution. Usually, the shape of the domains is at random or depends on the size and geometry of the sample. [3][4][5] In these instances there is no correlation between the relative orientation of the domains and the crystal lattice. For a few systems, however, the orientation and anisotropy of the crystal lattice matter. To explain the shape and orientation of the domains, in some of these cases the anisotropy of the spin stiffness must be taken into account, 6,7 while in others only certain spatial orientations of the domain walls minimize the sum of the magnetostatic stray-field energy and the magnetocrystalline anisotropy energy. 8 In this Rapid Communication we report on a different mechanism on how the domain-wall orientation is linked to the crystal lattice. For an ultrathin Fe film, we found out that the Dzyaloshinskii-Moriya interaction ͑DMI͒ plays the crucial role accounting for the orientation of the walls and further for the type of the wall and the rotational direction of the magnetization in the wall. The DMI is an antisymmetric exchange interaction that favors spatially rotating magnetic structures of a specific rotational direction.9,10 It vanishes in inversion-symmetric crystal structures; therefore, it can be excluded for most simple bulk materials. In surface or interface geometries, however, the inversion symmetry is broken and the DMI may become relevant.11 In a recent work 12 it was demonstrated for the first time that on some surfaces the DMI is so strong that it even dominates over the symmetric exchange interactions and induces a spatially rotating magnetic ground state.In this study, we describe the domain walls by a micromagnetic model in which the DMI is included. In contrast to earlier work, we determine all model parameters quantitatively from their electronic origin by first-principles calculations and thus we are able to draw conclusions on th...

Using spin-polarized scanning tunneling microscopy we show that the magnetic order of 1 monolayer Mn on W(001) is a spin spiral propagating along h110i crystallographic directions. The spiral arises on the atomic scale with a period of about 2.2 nm, equivalent to only 10 atomic rows. Ab initio calculations identify the spin spiral as a left-handed cycloid stabilized by the Dzyaloshinskii-Moriya interaction, imposed by spin-orbit coupling, in the presence of softened ferromagnetic exchange coupling. Monte Carlo simulations explain the formation of a nanoscale labyrinth pattern, originating from the coexistence of the two possible rotational domains, that is intrinsic to the system. DOI: 10.1103/PhysRevLett.101.027201 PACS numbers: 75.70.Ak, 68.37.Ef, 71.15.Mb Magnetism-based data storage technology relies on the fact that information, i.e., the magnetic state of the area representing the bits, is stable over time. From the microscopic point of view, the direction of the magnetic moments is stabilized mainly by the spin-orbit interaction, which couples the spin to the crystal lattice and is responsible for the occurrence of easy and hard magnetization axes. Based on this picture, the need for nanoscale magnetic devices called scientists to the quest for high magnetic anisotropy materials (see, e.g., Ref.[1]).However, with decreasing magnetic bit sizes the structural inversion asymmetry of interfaces and surfaces comes into play. A surprising consequence of this fact was recently demonstrated [2], namely, that this symmetry breaking in combination with spin-orbit coupling (SOC) leads to the Dzyaloshinskii-Moriya interaction (DMI) favoring noncollinear magnetic order [3,4]. Although the DMI, because of its relativistic nature, is usually expected to be negligible compared to the nonrelativistic exchange interaction, it is sufficiently strong to impose a nanoscale leftrotating cycloidal spin spiral (SS) on the otherwise antiferromagnetic Mn monolayer on W(110): adjacent moments slightly deviate from the collinear configuration by about 7 , resulting in a long-period SS [2].Many open issues of this new phenomenon remain. In noncentrosymmetric bulk materials the DMI is the origin of the weak ferromagnetism of parent antiferromagnets [4]. What are the consequences of the DMI in thin films possessing ferromagnetic exchange coupling, e.g., can it destabilize a ferromagnetic state? And what happens to the long-range magnetic order if SS's of different propagation directions are energetically degenerate due to symmetry? Can the DMI modify the magnetic order even on the atomic scale?As shown in this Letter, 1 ML Mn=W 001 is an ideal system to address these points: As opposed to the antiferromagnetic Mn=W 110 , this system exhibits strong ferromagnetic exchange interaction [5] and a fourfoldsymmetric square surface lattice. Spin-polarized scanning tunneling microscopy (SP-STM) measurements reveal a SS, i.e., magnetic moments rotating continuously from one atom to the next, propagating along h110i directions with a period ...

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